Auxiliary losses are commonly used in kinematic motion generation settings to improve physical realism in the absence of true simulation [1]}, [2]}, [3]}.
In addition to the reconstruction loss \(\mathcal {L}_\text{simple}\) , we adopt auxiliary losses similar to those in Tevet et al. [4]}, which encourage matching three aspects of physical realism: joint positions (eq:3), velocities (eq:4), and foot velocities via our Contact Consistency Loss (eq:5).
\( {\mathcal {L}_\text{joint} = \frac{1}{N} \sum _{i =1}^{N} \Vert  FK(\mathbf {x}^{(i)}) - FK(\mathbf {\hat{x}}^{(i)})\Vert _{2}^{2} }\) 
\( {\mathcal {L}_\text{vel} = \frac{1}{N-1} \sum _{i =1}^{N-1} \Vert  (\mathbf {x}^{(i+1)} - \mathbf {x}^{(i)}) - (\mathbf {\hat{x}}^{(i+1)} - \mathbf {\hat{x}}^{(i)})\Vert _{2}^{2}}\) 
\( {\mathcal {L}_\text{contact} = \frac{1}{N-1} \sum _{i =1}^{N-1} \Vert  (FK(\mathbf {\hat{x}}^{(i+1)}) - FK(\mathbf {\hat{x}}^{(i)})) \cdot \mathbf {\hat{b}}^{(i)}\Vert _{2}^{2}},\) 
